The situation reminded me of one of the strips from PHD Comics, about questions you shouldn't ask a graduate of a certain subject area. Well, it wasn't a tough question, but my answer (a haphazard description of the distinction between umlauts and diareses - and their varied usage) was far from suitable (I think they were more confused afterwards).
Nevertheless, the conversation moved on and all was well. I decided to look up the surname Brontë on wikipedia, and found a very interesting origin for the surname, and the 'ë':
"The Brontë family can be traced to the Irish clan mac Aedh Ó Proinntigh, which literally means 'son of Aedh, grandson of Proinnteach'. Aedh is a male name derived from Aodh, meaning "fire". "Proinnteach" ("the bestower") originated as a byname for a generous person. Literally meaning "banquet hall", the word is composed of the Gaelic proinn ("banquet") (a cognate of the Latin prandium ["meal"]) and teach ("house", "hall").
Ó Proinntigh was earlier anglicised as Prunty and sometimes Brunty. At some point, the father of the sisters, Patrick Brontë (born Brunty), conceived of the alternate spelling with the dieresis over the terminal "e" to indicate that the name is of two syllables. It is not known for certain what motivated him to do so, and multiple theories exist to account for the change. He may have wished to hide his humble origins. As a man of letters, he would have been familiar with classical Greek and chosen the name after the cyclop Brontes (literally 'thunder')."
I would not have guessed that Brontë was Irish in origin. It is interesting that it is one of the only common uses of the diaresis in English I can think of (besides its use in the New Yorker style guide for words such as 'reëlected').